Spatially periodic coupling for modes having differing propagation constants and traveling wave tube utilizing same



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Sept. 15, g. c... |v|||..|. .l.' r( SPATIALLY PERIODIC COUPLING FORMODES HAVING DIFFHRINC:

PROPAGATION CONSTANTS AND TRAVEIJTNG WAVE TUBE UTILIZING SAME Filed 001.21, 1968 6 ShGOtS-ShQOt l k dz Z{7\m=SPAT1AL PERIOD OF COUPLING FIG. 3

FIRST OUTPUT WAVE,V1

SECOND OUTPUT WAVE,V2-

(FIRST MODE) WEAK PASSIVE (SECOND MODE) F/GZ FIRST INPUT WAVE,W1

SECOND INPUT WAVE,W2

INVENTOR By S. [.M/LLE/P A T Tom/Er Sept. 15, 1970 s. E. MILLER3,529,205

SPATIALLY PERIODIC COUPLING FOR MODES HAVING DIFFERING PROPAGATIONCONSTANTS AND TRAVELING WAVE TUBE UTILIZING SAME 6 Sheets-Sheet 2 Filed001;. 21, 1968 36$ 54 w N lwl j 2 Q 2i 3,529,205 SPATIALLY PERIODICCOUPLING FOR MODES HAVING DIFFERING s. E. MILLER Sept. 15, 1970PROPAGATION CONSTANTS AND TRAVELING WAVE TUBE UTILIZING SAME 6SheetsSheet 5 Filed Oct. 21 1968 m 3 Sa o Sept. 15, 1970 s. E. MILLER 3,

' SPATIALLY PERIODIC COUPLING FOR MODES HAVING DIFFERING PROPAGATIONCONSTANTS AND TRAVELING WAVE TUBE UTILIZING SAME Filed Oct. 21, 1968 eShe0ts-Sheet 4 OUTPUT WAVE OUTPUT p 15, 1970 s. E. MILLER 3,529,205

SPATIALLY PERIODIC COUPLING FOR MODES HAVING DIFFMRING PROPAGATIONCONSTANTS AND TRAVELING WAVE TUBE UTILIZING SAME Filed 0012. 21, 1968 6Sheets-Sheet 5' N T a m at Sept 15, 1976 s. E MILLE 0 SPATIALLY IODIC CING FOR AVING DIFFERING NTS OUPL ES H PA A ION COI\ AND TRAVELING VETUBE ILIZING SAME Filed Oct. 21, 1968 6 Sheets-Sheet 6 FIG. 7

United States Patent 3,529,205 SPATIALLY PERIODIC COUPLING FOR MODESHAVING DIFFERING PROPAGATION CON- STANTS AND TRAVELING WAVE TUBE UTI-LIZING SAME Stewart E. Miller, Middletown Township, Monmouth County,N.J., assignor to Bell Telephone Laboratories, Incorporated, MurrayHill, N.J., a corporation of New York Filed Oct. 21, 1968, Ser. No.769,108 Int. Cl. H01j 25/34; H01p 3/20, 5/08 US. Cl. 315-35 22 ClaimsABSTRACT OF THE DISCLOSURE In a passive directional coupler with orwithout mode conversion, optimum transfer of energy from a first wavehaving a propagation constant k, to a second wave having a propagationconstant k is obtained by means of a weak coupling coefiicient which hasa spatial periodicity A given by:

FIELD OF THE INVENTION This invention relates to electromagnetic wavedirectional couplers with or without mode conversion, and in particular,to couplers for coupling waveguide modes having differing propagationconstants.

BACKGROUND OF THE INVENTION In many electromagnetic wave transmissionsystems, a first mode is relatively easy to excite but relativelydifficult to propagate efiiciently, whereas a second mode is relativelydifficult to excite but relatively easy to propagate efiiciently. Thesefirst and second modes generally have different propagation constants,and may exist in the same physical waveguide or in physically distanctfirst and second waveguides, respectively. It is therefore desirable tohave a way for coupling these modes in order to convert electromagneticwave energy originally excited and propagating in the first mode intoelectromagnetic energy propagating in the second mode.

In the prior art, as exemplified by my previous US. patents, such as2,748,350 issued on May 29, 1956; 2,820,- 202 issued on Jan. 14, 1958;2,948,864 issued on Aug. 9, 1960; and 3,020,495 issued on Feb. 6, 1962;ways for coupling such first and second modes are described. However,for maximum transfer of energy from the first to the second mode, thefabrication of appropriate coupling means hitherto has been ratherdifficult, requiring complicated and expensive shaping of the waveguidewalls. This complication arises, among other factors, from the necessityof satisfying certain relations between the coupling coeflicient C andthe difference in propagation constants (k k between the first andsecond modes.

SUMMARY OF THE INVENTION "present in distinct first and second mutuallycoupled waveguide structures. By weak coupling is meant that the amountof energy transferred from one mode to the other during any singlespatial period A of the coupling co- Patented Sept. 15, .1970

MM n-n (1) It should be understood that the 1 sign in Eq. 1 is'chosen inorder to make the spatial period A a physically meaningful (positive)quantity. Likewise it should be understood that even if Eq. 1 is onlyapproximately satisfied, nevertheless appreciable energy transferfcanoccur.

In general, for a given first and a given second mode, Eq. 1 issatisfied exactly only for a single frequency f Thus, appreciable energytransfer from one mode to the other occurs for a range of frequenciescentered at f". The bandwidth of this range of frequencies isapproximately inversely proportional to the number N of spatial periodsk in the coupling. On the other g'hand, the amount of energy transfer atf is approximately directly proportional to N. Thus, frequencyselectivity as well as the amount of energy transfer from one mode tothe other, both increase as the umber N of spatial periods k in a giventype of coupling is increased. Hence, a directional coupler structure,with a weak but spatially periodic coupling coefficient in accordancewith the above Eq. 1, can be also used as a bandpass filter inaccordance with another aspect of this invention. In such a case,increasing the number N of the spatial periods A in the couplingcoefiicient C is associated with narrowing the bandpass and increasingthe efficiency.

In terms of the dissimilar (unequal) propagation constants k, and k ofthe first and second modes, it is obvious from Eq. 1 that the spatialperiod k for maximum energy transfer may also be expressed as:

X =i27I'/'(k1k2) Of course, if a spatially periodic coupling weakcoefficient C merely contains a significant Fourier compo-.

PMM im- (1A) with p=odd integer (1B) More generally, especially in caseswhere the propa= gation constants k, and k are functions of positionalong the waveguide(s), the quantities A, and M as well as k; and kappearing in Eqs. 1 and 2 above should be regard as the averages ofthese respective quantities, Thus, the spatial periodicity k of thecoupling willin all events correspond to a distance along thewaveguide(s) over which the first mode undergoes a phase change whichdiffers by L2-rrp relative to the phase change of the second mode, withp being an odd integer.

The explanation of energy transfer by means of a periodic couplinginteraction may be easily understood by considering the eifect of thistype of interaction between the first mode and the second mode. Thecoeflicient of coupling C produces an interaction between those modesalong a distance (from to L) parallel to the propogation direction ofthe modes, which causes a transfer of energy from the first to thesecond mode. This energy transfer, in the absence of losses, isproportional to the square of:

L ik z ik z f +i k k 2 f 6 2 (C21) 0 C216 1) d2 (3) where z is theposition coordinate along the direction of propagation. See, forexample, Eq. 8 in my previous US. Pat. No. 2,748,350 issued on May 29,1956. Thus, maximum energy transfer will be obtained if C contains anexponential factor e which cancels the factor etllkrkllz in theintegrand, and thereby maximizes the value of the integral in Eq. 3. Inview of the identity:

there will also be significant energy transfer if the couplingcoefficient C has any, significant Fourier component with spatialperodicity A given at least approximately by Eq. 2 above. In such cases,this Fourier component will resonate at least approximately with thefactor e appearing in the integrand of Eq. 3 above thereby aifordingsignificant transfer of energy. However, the maximum amount of energytransfer for a given maximum coupling coefficient is obtained in caseswhere the coupling coefficient of C itself satisfies:

C -=iC[cos (k -k1)zi sin (k k )z] where C is a (coupling) constant.

It has been found by calculation that the previously known results ofthe theory of spatially constant coupling applies to spatially periodiccoupling having N spatial periods equal to A provided that the quantityis substituted for (kg-k1) in the previous results. Assuming no loss,for example, the energy transfer in a For definitiveness in algebraicsigns, it has been assumed that k is greater than k in this Eq. 8. FromEq. 2 above, it can be seen that D=0 at midband according to thisinvention, so that complete transfer (E =l) occurs provided the length Lalong the coupling structure sat- Furthermore, for complete transfer atmidband f in a coupling structure satisfying this Eq. 9, the first nullin the transfer occurs at frequency f (differt it from f which makes/1|D equal to 2, i.e., D= /3. In view of the fact that the magnitude of(f -f increases from zero monotonically with (k k -21r/)\ in thiscoupling structure satisfying Eq. 9 above, larger values of C (smallervalues of N) will yield this value of D= /3 for larger values of themagnitude of (f -f Hence larger values of C (smaller value of N) areassociated with broadband co. pling, whereas smaller values of C (largervalues of are associated with narrowband coupling, with completetransfer at midband.

Even if Eq. 9 above is not satisfied at midband (D=0) in this invention,nevertheless significant although not complete energy transfer occurs inaccordance with Eq. 7 above which may be rewritten for convenience as Ingeneral, again broadband coupling will be obtained (for fixed CLproduct) by means of relatively small values of N; and narrowbandcoupling will be obtained by means of relatively large values of N,where whether or not an integer.

A purely spatially sinusoidal type of coupling C =iC sin 21rz/)\ alsoyields results substantially the same as previously found for constantcoupling provided that k -k 21r/ is substituted for k k and an effectivecoupling coefiicient equal to C/2 is substituted for the constantcoefficient appearing in the previous results. Thus, spatiallysinusoidal coupling yields similar results as the exponetial couplingexpressed in Eq. 6 above, including the complete transfer conditionexpressed in Eq. 9 (but now substituting the effective couplingcoefficient C/2 for C therein).

For a square wave type of spatially periodic coefficient of couplinghaving spatially alternating values of +C and C, or 0 and 2C,calculations have shown that the previously known results for constantcoupling are obtained provided that (k k is replaced by 2 m 2 a -ea) andthe coupling constant replaced by an effective coupling coefiicientequal to 2C/ 11'. In view of the weak coupling used in this invention,Ch is small compared with unity and may be neglected under this squareroot. Thus, square wave spatially periodic Weak coupling leads to Eq. 2above at midband, at least in the weak coupling approximation. Moreover,square wave spatially periodic coupling yields similar results as theexponential coupling expressed in Eq. 6 above, including the completetransfer condition expressed in Eq.. 9 above (but now substituting theefifective coupling coeflicient 2C/ 1r for C therein).

In those embodiments of this invention in which it is desired to couplethe modes in two physically distinct waveguides, spatially periodiccoupling may be achieved for example by means of a spatially periodicarray of slots in a common wall between the waveguides. On the otherhand, in those embodiments of this invention in which it is desired tocouple the modes supported in the same single physical waveguide,periodic coupling may be achieved for example by introducing a spatiallyperiodic perturbation produced by dielectric sheets. In all cases,according to this invention, the spatial periodicity satis= fies Eq. 1above at the midband frequency, f Moreover, spatially periodic, weak,passive coupling according to this invention may be used to couple themodes of any waves having different propagation constants, such as theelectron space charge wave and the slow electromagnetic wave in atravelling wave tube.

This invention, together with its features, advantages, and objects maybe better understood from the following detailed description when readin connection with the drawings in which:

FIG. 1 is a general schematic illustration of the spatially periodiccoupling according to this invention;

FIG. 2 is a front view of a rectangular and a circular Waveguide whichsupport modes having different propa gation constants to be coupledaccording to this invention;

FIG. 2A is a cross-sectional view showing the spatially periodiccoupling slots in the common waveguide wall between the rectangular andcircular waveguides illustrated in FIG. 1, according to a specificembodiment of this invention;

FIG. 2B is a cross-sectional view showing the spatially periodiccoupling slots in the common waveguide wall between the rectangular andcircular Waveguides illustrated in FIG. 1, according to another specificembodiment of this invention;

FIG. 3 is a front view of circular waveguides, with spatially periodiccoupling in the common wall illustrated in the cross-sectional view ofFIG. 3A, according to another specific embodiment of this invention;

FIG. 4 is a perspective view of a circular waveguide with spatiallyperiodic coupling according to still another specific embodiment of thisinvention;

FIG. 4A is a perspective view of a rectangular waveguide with spatiallyperiodic coupling according to still another specific embodiment of thisinvention;

FIG. 5 is a front view of a dielectric waveguide structure, Withspatially periodic coupling illustrated in FIG. 5A, or FIG. 5Balternatively, according to still other alternate specific embodimentsof this invention;

FIG. 6 is a perspective view of a dielectric waveguide structure, withspatially periodic coupling according to yet another specific embodimentof this invention;

FIG. 7 is a front view of a dielectric waveguide structure with.spatially periodic coupling illustrated in side view FIG. 7A, accordingto another specific embodiment of this invention; and

FIG. 8 is a schematic side view, partly in cross-section, of atravelling Wave tube structure, with spatially periodic couplingaccording to yet another specific embodiment of this invention.

DETAILED DESCRIPTION The general schematic illustration of thisinvention is shown in FIG. 1. A First Input Wave W1 and a Second InputWave W2 are incident upon first and second waveguides 1 and 2respectively. It should be understood that the waveguides 1 and 2 shownin FIG. 1 may form a single waveguide structure which supports the Firstand Second Modes in the same physical space within the waveguidestructure.

In general, the First and Second Input Waves have the same frequency andare mutually coherent, although in some applications one of these InputWaves may contain no wave energy at all. The First Input Wave excites,among others, a First Mode in waveguide 1 having a guide wavelength xwhile the Second Input Wave (if any) excites, among others, a SecondMode in waveguide 2 having a guide wavelength A These First and SecondModes are coupled by means of the Spatially Periodic Weak PassiveCoupler 3, so that energy is transferred between these Modes. Thespatial period in the coupling coefiicient in the Coupler 3 is a asgiven by Eq. 1, or its equivalent Eq. 2, above. As a result, the FirstOutput Wave VI exiting from the first waveguide 1 has a differentamplitude and intensity from the First Input Wave W1; and the SecondOutput Wave W2 exiting from the second waveguide 2 has a differentamplitude and intensity from the Second Input Wave W2. In other Words,energy is transferred between the First Wave and the Second Wave. Energyat every frequency is conserved throughout (except for loss incidentalto the wave= guides 1 and 2 or the Coupler 3), i.e. the Coupler 3 ispassive and may utilize linear materials or means for coupling.

It should 'be emphasized again that the amplitude and intensity of theSecond Input Wave may be zero, especially in cases where it is desiredto convert available wave energy in the First Mode into Wave energy inthe Second Mode.

It should be appreciated that the arrangement shown in FIG. 1 may alsobe used as a band filter, in view of the fact that the relation given byEq. 1 for maximum energy transfer will be satisfied exactly only for asingle frequency i and will be satisfied even approximately only for aband of frequencies. Thus, appreciable energy will be transferred fromone wave to the other only for those frequencies within the band, byreason of the transfer of wave energy from the First Mode to the SecondMode, for example. Consequently, the arrangement shown in FIG. 1 may beused as a bandpass filter, in which the spatial periodicity in theCoupler 3 satisfies Eq. 1 above at midband. As used as such a filter,for example, the First Input Wave W1 contains the wave energy to befiltered, and the Second Input Wave W2 contains no Wave energy at all.After passage through the Waveguides 1 and 2 with the Spatially PeriodicCoupling 3, the Second Output Wave V2 will contain appreciable waveenergy at only those frequencies which are in the pass band. Thehalfwidth of this pass band is reduced by increasing the number N ofspatial periods of length A While the amount of energy in the pass bandtransferred from the First to the Second Wave, hence the couplingefficiency, is directly proportional to N.

FIG. 2 illustrates the front view of a first hollow metallic rectangulartubular waveguide 21 coupled to a second hollow metallic circulartubular waveguide 22 by means of slots 23 in the common Wall betweenthese waveguides 21 and 22. A thin dielectric lining 22A breaks the TETE degeneracy in these circular modes in the circular waveguide 22. Thedetails of the slots 23 are shown in the cross-sectional view FIG. 2A.In accordance with this invention, these slots 23 produce a spatiallyperiodic coupling, of the type embodied in Eq. 5 above, between therectangular electromagnetic TE mode in the rectangular waveguide 21 andthe circularly symmetric electromagnetic TE mode of the circularwaveguide 22. The longitudinally magnetic intensity H of both thesemodes are mutually weakly and passively coupled by the horizontal slotswhich are located off the centerline z axis, at positions which areequidistant from this centerline but each interval A /Z on oppositesides thereof. Moreover, the transverse magnetic intensity of the saidrectangular TE mode is coupled to the longitudinal magnetic in-= tensityof the said circular TE mode by means of the onaxis slots making anangle of 45 with the z-axis. The magnitude of the coefficient of thecoupling C at any location is proportional to the areas of the slots inthe neighborhood of the location. Advantageously, these areas of theslots are made to produce the sinusoidal variation in C as a function of2, this variation having a spatial period a given by Eq. 1 or itsequivalent Eq. 2 above. It should be understood that in Eq. 1, A is nowthe wavelength constant of the rectangular TE mode of waveguide 21,whereas 1 is the wavelength constant of the circular TE mode ofwaveguide 21.

A sinusoidal spatial variation in C entails a change in sign (phasereversal) every half-period interval A /Z. The phase reversal in thecoefiicient of coupling C to be produced by the off-axis slots, isrealized in FIG. 2A by successive reversals (every A /Z) of the slotposition With respect to the centerline z axis; whereas the phasereversal in the coefiicient of coupling, to be produced by the on-axisslots, is realized in FIG. 2A by reversal (every A /Z) of the slantangle of the slots from +45 to -45 with respect to the centerline zaxis. These phase reversals are ultimately produced by the interactionof the reversal of slot position with the phase of the coupled magneticintensity in the rectangular TE mode. Also, the spatial phase differenceinherently existing between the sine and the cosine term in the couplingcoefficient C is realized in FIG. 2A by having the on-axis slotsarranged out of spatial phase with respect to the ofi-axis slots; thatis, the maximum sized on-axis slots occur at the same value of z as theminimum sized off-axis slots, and vice versa. Finally, the difference bythe factor (-i) between the sine and cosine terms in C as given in Eq. 5above, is realized by the 90 phase difierence in the rectangular modesof the coupled magnetic fields themselves, ofi-axis vs. on-axis.

Instead of the coupling coeflicient C having the form embodied in Eq.and realized by the structure shown in FIG. 2A, FIG. 2B shows asymmetrical square wave type of coupling produced by the illustratedconfiguration of slots in the common wall between the rectangularwaveguide 21 and the circular waveguide 22. This arrangement is alsouseful. for coupling the electromagnetic rectangular TE mode ofwaveguide 21 with the circular electromagnetic TE mode of waveguide 22.The change in sign of symmetrical square wave coupling is produced byreason of the successive arrangement as shown in FIG. 2B of eachhalf-period interval (k 2) of substantially identical slots alternatelyon opposite sides of the centerline and equidistant therefrom, incombination with the opposite phase of the coupled longitudinal magneticintensity in the rectangular TE mode on alternate sides of thiscenterline z axis.

In using the periodic coupling structure illustrated in FIG. 2 as adirectional coupler with the common-wall slot configuration shown ineither FIG. 2A or FIG. 2B, in one particularly useful application, theinput wave is incident upon the rectangular waveguide 21 and the usefuloutput wave exits from the circular waveguide 22. In this way, the inputwave excites the rectangular TE mode in waveguide 21, and thisrectangular TE mode in turn excites the circular TE mode in waveguide22. This latter excitation of the circular TE mode occurs mostefficiently if the spatial period of the distribution of slots in thecommon Wall satisfies Eq. 1 above. Thus, the more easily excitedrectangular TE mode in the Waveguide 21 is converted into the moreeasily transmitted circular TE mode in the waveguide 22.

Coupling of other modes may be achieved with waveguide couplingstructures shown in FIG. 2B, so long as the mathematical product of thecoupled fields in the coupled modes is nonzero at the location of theslots and Eq. 1 is satisfied, according to the invention.

The embodiment illustrated in FIG. 3 shows a first circular hollowmetallic tubular waveguide 31 and a second circular hollow metallictubular waveguide 32 with a common wall therebetween. In this commonwall are located a spatially periodic array of discrete substantiallyidentical circular slots 33, for weakly and passively coupling the modesin the waveguides 31 and 32, as shown for example in FIG. 3A. Thesecircular slots 33 are present only at. every other spatial intervalequal to a half-period (A /2) along the common wall between the circularwaveguides 31 and 32, thereby giving rise to the spatial periodicity kof the coupling. The circular slots 33 are otherwise mutuallyequidistant and produce a raised square wave type of periodic coupling.In accordance with the invention, the spatial period k of the array ofslots is given by Eq. 1, where now A and X are the guide wavelengths ofthe first and second modes, the first mode in waveguide 31 to be coupledto the second mode in waveguide 32. For example, the first mode is themore easily excited circular TE and the second mode is the more easilytransmitted circularly symmetric TE Advantageously, dielectric linings31A and 32A break up the degeneracy between the circular TM and TE inthe waveguides 31 and 32, respectively.

The distance between centers of discrete neighboring slots in a givenhalf-period A /Z, as shown in FIG. 3A, advantageously is not more thanapproximately one-third the wavelength in either of the waveguides 31and 32. In this way, the type of coupling produced by this configurationof slots closely approximates that of raised square wave. The discreteslots may be used to couple any modes in waveguides 31 and 32 which havea nonvanishing math ematical product of field strengths to be coupled atthe lo cation of the slots. Just as in the embodiment shown in FIG. 2,the waveguides 31 and 32 coupled as shown in FIG. 3A may also be usedfor filtering purposes.

The embodiment illustrated in FIG. 4 shows a circular hollow metallictubular waveguide 41 with spatially periodical coupling for first andsecond modes within the same physical waveguide structure. Inparticular, the spatially periodic coupling is produced by substantiallyidentical thin dielectric coupling sheets 42 and 43, all of length X /Z,located on successive alternate sides with respect to a plane containinga diameter of the waveguide 41. In accordance with this invention, itshould be understood that a satisfies Equation 1 above at midband. Thedielectric constant of the coupling sheets 42 and 43 is significantlygreater than that of the surrounding space in the tubular waveguide 41,in order to produce a significant pertubation and hence coupling ofmodes. Thereby a symmetrical square wave type of mode coupling isproduced with a spatial periodicity in accordance with the invention.This arrangement shown in FIG. 4 is useful, for example, for couplingthe more easily excited circular electromagnetic TE mode with the moreeasily propagated circular electromagnetic TE mode. For a waveguide 41of radius R, maximum coupling of these modes may be obtained by locatingthe dielectric sheets 42 and 43 at an average distance r from the axisof the waveguide 41 where the magnitude of the mathematical product ofthe coupled fields of these two modes is a maximum. The dielectriccoupling sheets 42 and 43 may be conveniently supported mechanicallyupon the wall of the waveguide 41 by relatively low dielectric foamsupport linings 42F and 43F.

Other modes may be similarly coupled in this invention by means ofcoupling configurations similar to that shown in FIG. 4, satisfyingEquation 1 at midband.

The embodiment illustrated in FIG. 4A shows a hollow tubular rectangularmetallic waveguide 44, with spatially periodic coupling provided bymeans of the substantially identical thin dielectric coupling sheets 45and 46, all of length x,,,/ 2 satisfying Equation 1 at midband. Againjust as in the example shown in FIG. 4, the dielectric constant of thesheets is significantly greater than that of the surrounding space inthe waveguide 44. Successive coupling sheets 45 and 46 are located inthe waveguide 44 successively on opposite sides of, but otherwiseequidistant from, the centerline of the rectangular waveguide 44.Thereby there is provided a symmetrical square wave type of periodicmode coupling. Denoting the width of the waveguide 44 by 2a, for maximumcoupling coefiicient for the particular modes rectangularelectromagnetic TE and rectangular electromagnetic TE the averagedistance d of the dielectric sheets 45 and 46 from the centerline of thewaveguide is equal to (0.392)a, that is, where the product of theinteracting coupled fields is a maximum.

Other modes may be similarly coupled in this invention by means ofcoupling configurations similar to that shown in FIG. 4A, satisfyingEquation 1 at midband, but with suitable modification in the location ofthe dielectric coupling sheets 45 and 46 with respect to the centerline.

FIG. 5 is a side view of a solid tubular dielectric waveguide structureembedded in a substrate 50, in which a first optical mode in the solidrectangular dielectric region forming the waveguide 51 is coupled to asecond optical mode in the solid rectangular dielectric waveguide 52 bymeans of an array of dielectric coupling elements, the di electriccoupling strips 53. These dielectric coupling strips 53 are arranged ina spatially periodic array, for example, as shown in the side view ofFIG. 5A. The dielectric strips 53 couple the y component of the electricfield in the first and second modes. Typically, the waveguides 51 and 52are made of a material having a dielectric constant significantly higherthan that of the substrate 50, in order to support the first and secondmodes in the waveguides. The coupling strips 53 also have a higherdielectric constant than the substrate 50; and they are allsubstantially identical and parallel except for a reversal of slantevery interval equal to k 2. These strips 53 may be deposited usingphotolithographic techniques upon the substrate 50.

The slant of the coupling strips 53 is, as just mentioned, periodicallyreversed every distance interval equal to A /Z along the waveguides 51and 52, This reversal of slant gives rise to a physical displacement,advantageously equal to A 2, between the first coupling strip in a givenspatial period A /Z and the last coupling strip in the previous spatialperiod (also X /Z). Here A denotes the approximate guide wavelength ofeither the first mode, or the second mode, or an average thereof.Moreover, A is selected to satisfy Equation 1 above at midband, inaccordance with the invention; where now A and A are the wavelengths ofthe first and second modes, respectively, in the waveguides 51 and 52,respectively.

The configuration shown in FIG. SA yields symmetrical square wave typeof spatially periodic coupling, in accordance with the invention, byreason of the spatially periodic change in algebraic sign of thecoupling coefficient produced by the periodic reversal in the slantdirection of the coupling strips 53.

Tapering the width of the coupling strips 54, as shown in FIG. 5B,sinusoidally with distance along the waveguides 51 and 52 may be used toyield sinusoidal type of spatially periodic coupling. The dielectricwaveguide structures with periodic coupling, as shown in FIG. 5A or FIG.5B, are useful for filtering the input wave of a laser beam, forexample, which has a nonvanishing y component of electric field E.

FIG. 6 shows in perspective a waveguide structure consisting of asubstrate 60 having a significantly lower dielectric constant than thewaveguides 61 and 62, in order to propagate optical waves in the firstand second modes, respectively. Dielectric coupling elements, thedielectric .sheets 63, are arranged to produce raised square wave typeofspatially periodic coupling with spatial period A at midband given byEq. 1 above. Here x, and A are the guide wavelengths at midband inwaveguide 61 and 62, respectively.

FIG. 7 shows the front view of solid rectangular dielectric rectangularwaveguides 71 and 72 which support first and second electromagneticmodes, respectively. Typically, these waveguides 71 and 72 aremechanically supported by relatively low dielectric material, such asfoamed material (not shown). The dielectric in the waveguides 71 and 72typically is polyethylene, which has a relatively high dielectricconstant in order to propagate the first and second modes. Thewaveguides 71 and 72 are dimensioned to support, respectively, thesefirst and second modes having nonvanishing electric fields in the ydirection. Typically, these modes are for waves in the microwave regionof the electromagnetic spectrum. Moreover, these modes are coupled bymeans of spatially periodic coupling slots in the dielectric couplingsheet 73, as shown in cross-sectional view FIG. 7A. These coupling slotsare all par allel except that their slant from right-to-left isperiodically reversed to a slant from left-to-right. This reversal ofslant takes place every distance interval equal to X /Z along thewaveguides. This gives rise to a displacement, advantageously equal to k2, between the first slot in a given spatial period A /Z and the lastslot in the previous ,spatial period t /2. Here, A denotes theapproximate guide Wavelength of either the first mode, or the secondmode, or an average thereof. Moreover, x is chosen to satisfy Eq. 1above at midband according to the invention; where now and x are theguide wavelengths of the first and second modes, respectively, thewaveguides 71 and 72, respectively.

The reversal of slant of the slots effectively reverses the algebraicSign of the coupling coefficient. Moreover, as shown in FIG. 7A, thethickness of the slots may be sinusoidally tapered with distance alongthe z axis of the waveguides, in order to produce a sinusoidal couplingcoefficient C Alternatively, sinusoidal coupling may be obtained bymeans of a sinusoidal taper of the thickness of the dielectric sheet 73in the x direction in conjunction with uniform thickness in the zdirection. Of course, if symmetrical square wave coupling is desired, nosuch tapering need be built into the slots in the coupling sheet 73; thespatially periodic reversal in slant direction of the slots alone isSufficient to reverse the sign of the coupling periodically. In anyevent, the coupling structure illustrated in FIG. 7A may be used forfiltering purposes, as generally described above in connection with FIG.1.

FIG. 8 shows a schematic side view, partily in crosssection of atravelling wave electron tube structure consisting of a slow-wavestructure, the helix 8-1, along which is launched an electromagneticwave mode from the input waveguide 82 to the output waveguide 84, asknown in the art. Spatially periodic metallic shielding 83 produces aspatial period k in the weak passive coupling (raised square wave type)between the electromagnetic wave and the electron beam in the regionwithin the helix 81. Typically, a signal to be amplified modulates theflux of this electron beam prior to its entry into this region, therebycreating a space charge wave mode in the electron beam in this region.

It should be understood that the shielding 83 is insulated electricallyfrom the helix 81. Here again, the spatial period )\m of the shielding83 is given by Eq. 1 above ac cording to the invention, where now x isthe wavelength of the electromagnetic wave along the helix 81 and A is:the wavelength of the space charge wave of the electron beam in thesaid region in the travelling wave tube 80. The periodic couplingfurnished by the arrangement shown in FIG. 8 is useful for obtainingoptimum transfer of energy from a space charge waves in the electronbeam to .the electromagnetic wave in case these waves have differentpropagation constants, hence different wavelengths, in the travellingwave tube 80. Indeed, complete transfer at midband may be obtained ifthe number N of spatial periods in the shielding 8-3 satisfies Eq. 9above.

Instead of the spatially periodic shielding 83, any type of spatiallyperiodic loss may be introduced in the travelling wave tube, having aspatial periodicity which satisfies Eq. 1 according to the invention.

While this invention has been described in terms of specificembodiments, it should be obvious that many modifications are possiblewithin the scope of the inven tion. For example, various other types ofreciprocal and nonreciprocal waveguides supporting various modes knownin the art may be used, with the spatially periodic coupling of twodissimilar modes in accordance with the invention; that is, with acoupling coefficient having a spatial periodicity which satisfies Eq. 1or its equivalent Eq. 2 above.

What is claimed is:

1. An electromagnetic wave coupler which comprises:

(a) first means for supporting first and second electromagnetic wavemodes having the same frequency and having unequal propagation constantsk and k respectively; and

(b) second means for weakly and passively periodical- 1y coupling saidfirst and second wave modes, said second means characterized by acoeflicient of cou pling of at least two spatial periods having asignifi cant Fourier component corresponding to a spatial periodicitysubstantially equal to the magnitude of 21I'/ (k -1(2)- 2. A wavecoupler according to claim 1 in which said spatial periodicity is equalto the magnitude of at midband.

3. A wave coupler according to claim 1 in which the said coefficient ofcoupling has a spatial periodicity equal to the magnitude of 21r/ k k atmidband.

4. A wave coupler according to claim 1 in which the effective couplingcoefficient multiplied by L is at least approximately equal to 1r/2,Where L is the length of the region in which said coupling coefficientexists.

5. A directional coupler according to claim 1 in which the first meanscomprise a first rectangular waveguide 1 1 for supporting the firstmode, and a second circular waveguide for supporting the second mode;and in which the second-mentioned means for coupling said first andsecond modes include an array of slots having said spatial periodicityin a common wall between said first and second waveguide means.

6. A directional coupler in accordance with claim 5 in which the firstmode is the rectangular electromagnetic TE mode and the second mode isthe circular electromagnetic TE mode.

7. A directional coupler in accordance with claim 1 in which the firstmeans comprise a first circular waveguide for supporting said firstmode, and a second circular waveguide for supporting said second mode;and in which the second-mentioned means for coupling said first andsecond modes include an array of slots characterized by the said spatialperiodicity in a common wall between said first and second waveguidemeans.

8. A directional coupler according to claim 7 in which said first modeis the circular electromagnetic TE and said second mode is the circularelectromagnetic TE 9. A directional coupler according to claim 1 inwhich the first means comprise a circular waveguide which can supportsaid first and second modes, and in which the second-mentioned means forcoupling said first and second modes includes an array of dielectricsheets located within said circular waveguide.

10. A directional coupler in accordance with claim 9 in which eachdielectric sheet in said array is situated with respect. to itsneighboring sheet on the opposite side of a plane containing a diameterof said circular waveguide; and in which the first mode is the circularelectromagnetic TE and the second mode is the circular electromagnetic TE 1.

11. A directional coupler according to claim 1 in which the first meanscomprise a rectangular waveguide which can support said first and secondmodes, and in which the second-mentioned means for coupling said firstand second modes include an array of dielectric sheets located withinsaid rectangular waveguide.

12. A directional coupler according to claim 11 in which each dielectricsheet is situated with respect to its neighboring sheet in the saidarray on the opposite side of a centerline of the said rectangularwaveguide.

13. A directional coupler in accordance with claim 12 in which saidfirst mode is the rectangular electromagnetic TE and said second mode isthe rectangular electromagnetic TE 14. A directional coupler inaccordance with claim 1 in which the first means include a first tubulardielectric region forming a first Waveguide and a second tubulardielectric region forming a second waveguide, and in which thesecond-mentioned means for coupling said first and second modes includean array of dielectric coupling elements.

15. A directional coupler in accordance with claim 14 in which saiddielectric coupling elements are essentially dielectric strips; all saiddielectric strips, within each interval along the first means equal toone-half the said spatial periodicity, being mutually parallel; and inwhich the dielectric strips in each said interval are slanted withrespect to the dielectric strips in a neighboring interval.

16. A direction coupler in accordance with claim 14 in which saiddielectric coupling elements comprise a plurality of dielectric sheets,each of said sheets having a length approximately equal to one-half thesaid spatial periodicity.

17. A directional coupler in accordance with claim 14 in which each ofsaid dielectric regions is embedded in a substrate having asignificantly lower dielectric constant than the dielectric constant ofsaid dielectric regions.

18. A directional coupler according to claim 1 in which the first meansinclude a first tubular dielectric region forming a first waveguide forsupporting the first mode and a second tubular dielectric region forminga second waveguide for supporting the second mode, and in which thesecond-mentioned means for coupling the said first and second modesinclude an array of slots in a dielectric coupling sheet.

19. A directional coupler according to claim 18 in which all said slotsare mutually parallel, within each interval along the first means equalto one-half the said spatial periodicity; and in which the said slots ineach said interval are slanted with respect to the slots in aneighboring interval.

20. In a travelling wave tube, a coupler Which comprises:

(a) means for providing a beam of electrons in said tube, said beamcharacterized by a space charge wave in a first mode having apropagation constant k (b) a slow electromagnetic wave structure forsupporting an electromagnetic wave in a second mode having a propagationconstant k said first and second modes being coupled with a spatiallyperiodic weak effective coupling coefiicient having at least two spatialperiods, the spatial periodicity along said tube of said coefiicienthaving a square wave type of spatial periodicity with a significantFourier com= ponent corresponding to a spatial periodicity at leastapproximately equal in magnitude to 21r(k -k 21. In a travelling wavetube, a coupler according to claim 20 in which the second means forcoupling the first and second modes include a spatially periodicshielding of the said slow electromagnetic wave structure from theelectron beam in said tube, said shielding characterized by the saidspatial periodicity.

22. In a travelling wave tube, a coupler according to claim 20 in whichthe effective value of the coupling coefiicient multiplied by L is atleast approximately equal to 1r/2, where L is the length of the regionin which said coupling coefficient exists.

References Cited UNITED STATES PATENTS 2,748,350 5/1956 Miller 33321 X2,834,944 5/1958 Fox 33310 2,926,281 2/1960 Ashkin 315-3.6 2,948,8648/1960 Miller 33310 3,238,473 3/1966 Salzberg 333-10 PAUL L. GENSLER,Primary Examiner US. Cl. X.R.

